An investment in an instrument.

For example, when you trade (say, buy) USDJPY, you open a USDJPY position.

When you then execute the opposite trade (in this case, sell) USDJPY, you close the position.

Position can also refer to a trader's cash/securities/currencies balance, whether he or she is short of cash, has money to lend, is overbought or oversold in a currency, etc.